simon-5507-02-slides

Topics to be covered

What you will learn
- Using variable labels
- Simple descriptive statistics
- Printing row with smallest/largest value
- Missing value logic
- Simple transformations
- Histograms
- Correlations
- Scatterplots

Review definitions

Categorical
- Small number of possible values
- Each value associated with a category
Continuous
- Large number of possible values
- Potentially any value in an interval

Before we start, let’s review a couple of definitions.

A categorical variable is a variable that can only take on a small number of values. Each value is usually associated with a particular category.

Examples of categorical variables are

sex (Male or Female),
race (White, Black, Native American, etc.),
cancer stage (I, II, III, or IV),
birth delivery type (Vaginal, C-section).

A continuous variable is a variable that can take on a large number of possible values, potentially any value in some interval.

Examples of continuous variables are

Birth weight in grams,
gestational age,
fasting LDL level.

There are some variables that are on the boundary between categorical and continuous, but it is not worth quibbling about here.

The point to remember is that the types of graphs that you use and the types of statistics that you compute are dependent on many things, but first and foremost on whether the variables are categorical, continuous, or a mixture.

Today, you will see examples involving mostly continuous variables.

Semicolons are important

Ends every SAS statement
Easy to forget
Use this to your advantage
- Several short lines
- Indent continuations

Example of stretching statement across multiple lines.

One long line

statement option1 option2 option3 option4;

versus several short lines.

statement
  option1
  option2
  option3
  option4;

The use of semicolons is nice, in a way, because it allows you to stretch a complicated SAS statement across two or more rows of your program. This can often make your program more readable. It is hard to read a long line of code. Your eye has to scan left to right and you can sometimes lose track of which line you are on. Most newspapers place their articles in narrow columns because it makes them easier to read.

There is no official rule of thumb on this, but I do try to keep my lines below 50 characters. I also try to indent substatements with a data step or procedure. I use blank lines between data steps and procedures.

Don’t obsess about this now, but you’ll see a fairly consistent coding style that I use for my SAS code. You don’t have to follow my format, of course, which might be a bit too extreme for your tastes. Just experiment with things a bit until you can settle on a layout that you are comfortable with.

Rules for variable names (1/2)

Can use mix of
- letters (A-Z, a-z),
- numbers (0-9)
- underscore (_)
- no blanks, no symbols

There are important rules for variable names in SAS. You can use a mix of letters, numbers, and the underscore. You can’t use blanks or any special symbols like the dollar sign ($) or the dash/minus sign.

I’m using the variable names provided but if you create your own names, use brief (but descriptive) name for EVERY variable in your data set. There’s no precise rule, but names should be around 8 characters long. Longer variable names make your typing tedious and much shorter variable names makes your code terse and cryptic.

I’m a bit more terse with these variable names than I normally would be just to reduce the amount of typing you have to do.

You should avoid special symbols in your variable names especially symbols that are likely to cause confusion (the dash symbol, for example, which is also the symbol for subtraction). You should also avoid blanks. These rules are pretty much universal across most statistical software packages.

Rules for variable names (2/2)

Can’t start with a number
- “a1” but not “1a”
Capitalization not important
- BMI, Bmi, bmi are same
Up to 32 characters in length

Recommendations for variable names (1/2)

Avoid generic names (x1, var01, etc.)
Keep it short
- Use commonly known abbreviations…
- …but nothing cryptic
Use all lower case (age, not AGE or Age)

Recommendations for variable names (2/2)

Separate words with underscores
- fat_brozek, not fatbrozek
Alternative: CamelCase
- FatBrozek
Caution: Writer’s Exchange website
- www.writersexchange.com

You can use two or three short words in a variable name, but be sure to separate them using underscores. So the variable for percentage body fat as measured by Brozek’s equation is “fat” and “brozek” separated by an underscore. Some people prefer CamelCase, where each word starts with an initial capital letter: capital F fat, capital B brozek.

The one thing you do want to avoid is just running two or three words together and all lower case. There’s a story about a group that started up in the era before the web called Writer’s Exchange. As you can guess this was a resource for new authors. When the web came out, they decided to put their resources up on a website, www.writersexchange.com. That seemed logical enough, but then someone notices that you could read the website as “www dot writer sex change dot com”. Not exactly the image they wanted.

SAS variable labels (1/2)

Longer description of a variable
- Can include blanks, special symbols
- Internal documentation
- Labels substituted on some (but not all) output
Required in this class (see grading rubric)

SAS variable labels (2/2)

Recommendations for variable labels
- Judicious use of upper and lower case
- Spell out abbreviations
- Specify units of measurement
- Any other important details

Documenting your program (1)

* 5507-02-simon-continuous-variables.sas
  author: Steve Simon
  date: created 2021-05-30
  purpose: to work with continuous variables
  license: public domain;

* datasets created in this program
    body, original data
    body1, row with ht=29.5 removed
    body2, ht=29.5 converted to missing
    body3, ht_cm calculated;

Specifying file locations (2)

%let path=q:/5507-2025b/02;

filename rawdata
  "&path/data/fat.txt";

libname module02
  "&path/data";

ods pdf file=
  "&path/results/simon-5507-02-demo.pdf";

Reading in the data (3)

data module02.body;
  infile rawdata;
  input 
    case
    fat_brozek
    fat_siri
    dens
    age
    wt
    ht
    bmi
    ffw
    neck
    chest
    abdomen
    hip
    thigh
    knee
    ankle
    biceps
    forearm
    wrist;

Adding labels (4)

label
    case="Case number"
    fat_brozek="Fat (Brozek's equation)"
    fat_siri="Fat (Siri's equation)"
    dens="Density"
    age="Age (yrs)"
    wt="Weight (lbs)"
    ht="Height (inches)"
    bmi="Body mass index (kg/m^2)"
    ffw="Fat Free Weight (lbs)"
    neck="Neck circumference (cm)"
    chest="Chest circumference (cm)"
    abdomen="Abdomen circumference (cm)"
    hip="Hip circumference (cm)"
    thigh="Thigh circumference (cm)"
    knee="Knee circumference (cm)"
    ankle="Ankle circumference (cm)"
    biceps="Biceps circumference (cm)"
    forearm="Forearm circumference (cm)"
    wrist="Wrist circumference (cm)";
run;

Adding extra information (5)

* Some additional details about this data:

  Brozek's equation is 457/Density - 414.2

  Siri's equation is 495/Density - 450

  Abdomen circumference is measured at the
  umbilicus and level with the iliac crest

  Wrist circumference is distal to the 
  styloid processes;

The footnote subcommand (6)

proc print
    data=module02.body(obs=10);
  var case fat_brozek fat_siri dens age;
  title1 "Ten rows and five columns";
  title2 "of the body data set";
  footnote1 "Created by Steve Simon on &sysdate using SAS &sysver";
run;

Displaying metadata (7)

proc contents
    data=module02.body;
  title1 "Internal description of body dataset";
run;

Live demo, 1

data step
- label subcommand
contents procedure

Break #1

What you have learned
- Using variable labels
What’s coming next
- Simple descriptive statistics

Simple descriptive statistics

Always look at first
Is mean high, normal, or low?
Is data spread out or tight?
- Zero standard deviation is a red flag
Are minimum and maximum reasonable?

You should always look at simple descriptive statistics first before embarking on any data analysis. This is especially true for very complex data analyses. Often the complex analyses are largely opaque and difficult to follow. You will have a better time understanding how the mixture of variables in these models behave if you first have an understand how each variable behaves individually.

First examine the mean relative to your expectations. Is it about what you’d expect or is it low or high relative to your expectations?

Look at the standard deviation. A rough rule of thumb is that about 68% of the data will lie within one standard deviation of the mean and that about 95% of the data will lie within two standard deviations of the mean. That won’t be true for highly skewed distributions, but it is still worthwhile to think about these calculations. Do they indicate that the data is widely spread or tightly packed?

Watch out for any variables that have zero for a standard deviation. This tells you that the data is constant (no variation), which would preclude that variable’s use in most data analyses.

Look at the minimum and maximum values. Are they extreme to cause concern? If they are outside the range of possible values, investigate. Maybe there is a data entry error.

Computing simple statistics (8)


proc means
    n mean std min max
    data=module02.body;
  var ht;
  title1 "Descriptive statistics for ht";
  title2 "The mean is normal for adults";
  title3 "The standard deviation shows tightly packed data";
  title4 "The maximum value is reasonable";
  title2 "The minimum is very low";
run;

Live demo, 2

means procedure
- n option
- mean option
- std option
- min option
- max option

Break #2

What you have learned
- Simple descriptive statistics
What’s coming next
- Printing row with smallest/largest value

Sorting your data

Uses the sort procedure
Specify the dataset with data=
Specify the sorting variable with the by subcommand
- Use descending keyword to sort in reverse order

Printing row with smallest or largest value

Investigate other variables associated with outlier
Is the data shifted left or right?
Are other values consistent with the outlier?

Printing row with smallest value (9)


proc sort
    data=module02.body;
  by ht;
run;

proc print
    data=module02.body(obs=1);
  title1 "The row with the smallest ht";
  title2 "Note the inconsistency with wt";
run;

Printing row with largest value (10)

proc sort
    data=module02.body;
  by descending ht;
run;

proc print
    data=module02.body(obs=1);
  title1 "The row with the largest ht";
  title2 "This seems quite normal to me";
run;

Live demo, 3

sort procedure
- by subcommand
  - descending option

Break #3

What you have learned
- Printing row with smallest/largest value
What’s coming next
- Missing value logic

What to do with outliers

Depends on the context, ask for help!
- Live with it
- Delete the entire observation
- Convert the value to missing

With this outlier on the low end, you might consider doing nothing other than noting the unusual value.

Alternately, you could delete the entire row associated with this value. Finally, you might consider converting the small ht value to a missing value code.

There is no one method that is preferred in this setting. If you encounter an unusual value, you should discuss it with your research team, investigate the original data sources, if possible, and review any procedures for handling unusual data values that might be specified in your research protocol.

Notice that I store the revised data sets with the row removed and with the 29.5 replaced by a missing value in different data frames. This is good programming practice. If you ever have to make a destructive change to your data set (a change that wipes out one or more values or a change that is difficult to undo), it is good form to store the new results in a fresh spot. That way, if you get cold feet, you can easily backtrack.

We’ll use the data set with the 29.5 changed to a missing value for all of the remaining analyses of this data set.

How to handle outliers

No option is best in all cases
- Live with them
- Remove the entire row
- Convert outlier to missing
Always report clearly

When you encounter outliers, you have several options. Often the best approach is to live with them. You might report both a mean and a median, for example.

You could remove a patient entirely from the analysis. This is a pretty radical step and should be done if you can argue that all of the patient’s data is hopelessly compromised. You might also argue that the patient clearly is ineligible for the study and should never have been let in.

You could also convert the outlier to a missing value. This is also a big step, but at least it allows you to use the rest of the data for that patient.

Generally, an extreme value by itself does not support removal of a patient or converting an outlier to missing. You need to provide external evidence. A notation in a lab notebook, for example, of sample handling problems, might justify this step. You could also remove an outlier if you could argue that the value is incompatible with life, such as a patient with a body mass index of 5.1.

Importing missing values

Different coding schemes
- dot (.) or blank ( ), the SAS standard
- other symbols (*, ?)
- NA, the R standard
- NULL, the SQL standard
- Extreme numbers (-1, 9, 99, 999)
- Blank ( ) or empty ()

Your data set may arrive with missing values in it already. Data might be designated as missing for a variety of reasons (lab result lost, value below the limit of detection, patient refused to answer this question) and how you handle missing values is way beyond the scope of this class. Just remember to tread cautiously around missing values as they are a minefield.

Missing data could be coded as a single dot (.), which is the SAS standard for missing numeric data. You might also see some other symbol such as an asterisk or a question mark. R uses NA for missing and SQL uses NULL.

You may see extreme numeric values, extreme meaning outside a reasonable range, as codes for missing values. A birthweight of -1, for example, probably indicates missingness, as a baby weighing -1 kilograms would float up to the ceiling after being born. Other times, of course, -1 would not work, such as when recording your checking account balance the day before payday.

Sometimes, one or more nines would indicate a missing value. A Likert scale item coded 1 for strongly disagree through 5 for strongly agree will often code a non-response as 9. Make sure you have enough nines. An IQ score would not use 99 as the missing code because that is a legitimate value. A code of 999 makes more sense here because even Albert Einstein’s IQ falls well below 999.

One or more blanks might represent missing or an empty field (a zero length string) might represent missing. I discourage the use of blanks or empty fields for several reasons. First, when your computer diplays a single blank, it looks just like an empty field. Second, an empty or blank field might represent not missingness, but rather that the data entry person has not gotten to enter that value yet. Third, some systems (not SAS) might convert an empty field to zero, which is often not what you want.

Advice on importing missing values

Read the data dictionary
Always ask WHY a value is missing
Convert any non-standard missing codes
- if iq=999 then iq=.

Missing value logic in SAS

Stored internally as most extremely negative number
- Approximately $-1.8 \times 10^{308}$ (on most computers)
Can identify with = . or missing()
- Differs from R
Use caution with less than/greater than comparisons
- age < 18 will include children AND missing ages
- use age ^= . & age < 18 instead

SAS stores missing values internally as the most extremely negative number. On most systems that would be -1.8 time ten to a ridiculously large number. It is more extreme than a negative googol (-1 times 10 to the 100 power) and far larger in absolute value than the number of atoms in the universe (approximately 10 to the 78 power or 10 to the 82 power). So you are unlikely to use such an extremely negative number in any real world calculations.

You can identify a missing value using the missing function or the = . comparison. This is handy. In R trying to use an equality comparison involving missing values will evaluate not to true or false but to missing. This produces a complex three valued logic system. In SAS, any equality comparison will produce either true or false and no third value. This has its advantages.

The disadvantage occurs when using less than and greater than comparisons. You might want to identify children in your dataset using age < 18, but this would include children and anyone in your dataset with a missing age. You should exclude missing values explicitly first before doing any less than or greater than calculations. That’s a good rule to follow in R as well.

Removing a row of data (11)


data module02.body1;
  set module02.body;
  if ht = 29.5 then delete;
run;

Converting outlier to missing (12)

data module02.body2;
  set module02.body;
  if ht=29.5 then ht=.;
run;

Printing negative values (wrong way) (13)

proc print
    data=module02.body2;
  where ht < 0;
  title1 "Printing negative values for ht (wrong way)";
  title2 "Use where ht ^= . & ht < 0 instead";

run;

Counting missing values (14)

proc means
    n nmiss mean std min max
    data=module02.body2;
  var ht;
  title1 "There is one missing value";
run;

Live demo, 4

set subcommand (data step)
if … then subcommand (data step)
where subcommand (proc)
nmiss option (means procedure)

Break #4

What you have learned
- Missing value logic
What’s coming next
- Simple transformations

Transforming values

Use data step to create a new variable
- Unit conversion: temperature = 5/9 * (temperature - 32)
- New variable: bmi = wt_kg / ht_m^2

Different variable, same data

data name1;
  set name1;
  wt_kg = wt / 2.2;
run;

Same variable, different data

data name2;
  set name1;
  wt = wt / 2.2;
run;

Transforming values (15)


data module02.body3;
  set module02.body;
  check_bmi = (wt / 2.2) / (ht / 39.37)**2;
  check_ht = sqrt((wt / 2.2) / bmi) * 39.37;
  check_wt = (bmi * (ht / 39.37)**2) * 2.2;
run;

proc print 
    data=module02.body3;
  var ht check_ht wt check_wt bmi check_bmi;
  where ht=29.5;
  title1 "Recalculating ht, wt, and bmi";
  title2 "Assuming two out of three are correct.";
run;

Reminder

$bmi = \frac{wt}{ht^2}$, if wt and ht correct
$ht = \sqrt{\frac{wt}{bmi}}$, if wt and bmi correct
$wt = bmi \times ht^2$, if ht and bmi correct
Don’t forget unit conversions!
- Converting inches to meter, $\times 39.37$
- Converting pounds to kilograms $\div 2.2$

Live demo, 5

No new keywords

Break #5

What you have learned
- Simple transformations
What’s coming next
- Histograms

Historial sidenote, IBM mainframe printer

Historical sidenote, Sample output from proc plot

Historical side note, box drawing characters

Box drawing characters

░   ▒   ▓   │   ┤   ╡   ╢   ╖   ╕   ╣   ║   ╗   ╝   ╜   ╛   ┐
└   ┴   ┬   ├   ─   ┼   ╞   ╟   ╚   ╔   ╩   ╦   ╠   ═   ╬   ╧
╨   ╤   ╥   ╙   ╘   ╒   ╓   ╫   ╪   ┘   ┌   █   ▄   ▌   ▐   ▀

Before box drawing characters

| - +

Historical side note, Pen plotter

Historical note, Dot matrix printer

Today’s technology, Ink jet or laser printer

300 dots per inch or better
Up to 16.7 million colors
- CMYK system versus RGB system

Today’s technology, 3D printers (SAS does not support these)

Drawing histograms

Histograms can assess normality/non-normality
- Skewness
- Bimodal distributions
- Outliers
How many bars? Multiple recommendations
- Five to twenty bars
- Square root of n bars
- Trial and error

A histogram can help you assess the distributional pattern of your data. Is it normally distributed (the classical bell shaped curve)? If so, you can make fairly strong assumptions about the data. The mean plus or minus one standard deviation will contain roughly 68% of the data. The mean plus or minus two standard deviations will contain roughly 95% of the data.

Normality is also an assumption needed for a variety of confidence intervals and hypothesis tests. It is not a life-or-death assumption, especially when your sample size is large. Also, the normality assumption is often better assessed using residuals from your statistical model.

The other nice thing about the histogram is that it can identify what type of deviation from normality you might have. Identifying bimodality is the trickiest, because if you have too few bars you might miss the gap between modes. If you have too many bars, you might see multiple modes because of the spikiness that is artificially produced when you have too many bars.

There is no simple rule for deciding how many bars you should have in your histogram. Once sources suggests that 5 to 20 is a reasonable number of bars. Another suggests that the number of bars should be roughly equal to the square root of the sample size. To be honest, the best approach might be to try several different choices and see which one gives a reasonable picture of the distribution of your variable.

Drawing a histogram (default) (16)


proc sgplot
    data=module02.body2;
  histogram ht;
  title1 "Histogram shows a roughly normal distribution";
  title2 "Default bins (not recommended)";
run;

Drawing a histogram (fewer bars) (17)

proc sgplot
    data=module02.body2;
  histogram ht / binstart=60 binwidth=5 nofill;
  xaxis values=(60 to 85 by 5);
  title "Histogram with wide bins (better)";
run;

Drawing a histogram (more bars) (18)

proc sgplot
    data=module02.body2;
  histogram ht / binstart=62 binwidth=1 nofill;
  xaxis values=(62 to 80 by 2);
  title "Histogram with narrow bins (best)";
run;

Live demo, 6

sgplot procedure
- histogram subcommand
  - binstart option
  - binwidth option

Break #6

What you have learned
- Histograms
What’s coming next
- Correlations

Correlations

Informal interpretation
- between +0.7 and +1.0: strong positive association
- between +0.3 and +0.7: weak positive association
- between -0.3 and +0.3: little or no association
- between -0.3 and -0.7: weak positive association
- between -0.7 and -1.0: strong negative association

The correlation coefficient is a single number between -1 and +1 that quantifies the strength and direction of a relationship between two continuous variables. As a rough rule of thumb, a correlation larger than +0.7 indicates a strong positive association and a correlation smaller than -0.7 indicates a strong negative association. A correlation between +0.3 and +0.7 (-0.3 and -0.7) indicates a weak positive (negative) association. A correlation between -0.3 and +0.3 indicates little or no association.

Don’t take these rules too literally. You’re not trying to make definitive statements about your data set. You are just trying to get comfortable with some general patterns that occur in your data set. A complex and definitive statistical analysis will almost certainly not agree with at least some of the preliminary correlations noted here.

The corr procedure produces, by default, a square correlation matrix of all the numeric variables. The noprob and nosimple options cut down on the amount of information printed. The with statement produces a rectangular correlation matrix.

Computing correlations (default) (19)



proc corr
    data=module02.body2
    noprint
    outp=correlations;
  var fat_brozek fat_siri;
  with neck -- wrist;
run;

Processing correlations (20)

data correlations;
  set correlations;
  if _type_ NE "CORR" then delete;
  drop _type_;
  fat_brozek=round(fat_brozek, 0.01);
  fat_siri=round(fat_siri, 0.01);
run;

Sorting the correlations (21)

proc sort
    data=correlations;
  by descending fat_brozek;
run;

proc print 
    data=correlations;
  title1 "Abdomen, hip, and chest show the strongest correlations";
run;

Live demo, 7

corr procedure
- noprint option
- outp option
- with subcommand
drop subcommand (data step)
round function

Break #7

What you have learned
- Correlations
What’s coming next
- Scatterplots

Drawing a scatterplot (22)


proc sgplot
  data=module02.body2;
  scatter x=abdomen y=fat_brozek /
    markerattrs=(size=10 symbol=circle);
  pbspline x=abdomen y=fat_brozek /
    lineattrs=(pattern=dash color=red);
  title1 "Simple scatterplot shows a strong positive trend";
  title2 "It levels off for high values.";
  title3 "This may be due solely to a single outlier on the high end";
run;

Closing the pdf file (23)

ods pdf close;

Summary

What you have learned
- Using variable labels
- Simple descriptive statistics
- Printing row with smallest/largest value
- Missing value logic
- Simple transformations
- Histograms
- Correlations
- Scatterplots